User inherits what the original guardian possessed; all their experiences, knowledge, abilities, powers, skills, and other features including possibly appearance, with each new generation becoming stronger through the achievements and progress of their predecessors.
The title of Promethea (Promethea) is passed on between hosts of the ancient immaterial spirit Promethea.
The Avatar (Avatar series) is reincarnated between nations, acting as the peacekeeper of the world and being the only person who can bend all four elements...
...Korra being the current Avatar.
Buffy Summers (Buffy, the Vampire Slayer) is the Slayer...
... whose death will turn one among many Potential Slayers into the official Slayer...
... until Willow Rosenberg changes the metaphysical law allowing all Potentials to become Slayers.
The Author (Once Upon a Time) is a title given to select individuals by the Sorcerer to record the events of the Enchanted Forest, given a magical-pen to accomplish this, but also have the power to influence the events however they see fit.
Terra (Kingdom Hearts) chooses Riku to succeed him as a Keyblade wielder.
Geomancers (Valiant Entertainment) are an ancestral tribe of aboriginal mystics who commune with and safeguard the world from various threats. Each time one who carries the title of Geomancer dies a new person in the world steps in to take their place.
After the death of Ariel, Kain (Legacy of Kain) was born specifically to take her place as the Balance Guardian of the Circle of Nine.
After the death of Sara, Seira (Mermaid Melody Pichi Pichi Pitch) was born to take her place as the Mermaid Princess of the Indian Ocean.
Pillars of Old Equestria (My Little Pony: Friendship is Magic)